No. In relativity, there are mathematical structures called the "manifold" and the "metric tensor". The metric tensor is an additional mathematical structure that is placed on the manifold. Conceptually, the manifold is like a fabric, and the metric tensor is like a system of rulers and clocks at every point on the fabric. What we call "spacetime" in relativity usually refers to the metric tensor, ie. the system of rulers and clocks which live on the fabric.

I want to know that whether space-time is like a large fabric spread through the universe and whether it is finite in size.

I'm a bit concerned that you haven't read (or at least having admitted to reading) any of the references that you were pointed towards.

How do you think one would tell if spacetime "was like a large fabric"?

If you asked something more specific like "Can space-time be cut", "Can spacetime be bent", "Can spacetime be stretched", "Can space-time be sewn together so you can make clothes out of it" (well, that one is a bit silly!) etc, we might be able to answer the question better. "Is it like a fabric" is rather ambiguous - is it like a fabric, how, exactly?

No. In relativity, there are mathematical structures called the "manifold" and the "metric tensor". The metric tensor is an additional mathematical structure that is placed on the manifold. Conceptually, the manifold is like a fabric, and the metric tensor is like a system of rulers and clocks at every point on the fabric. What we call "spacetime" in relativity usually refers to the metric tensor, ie. the system of rulers and clocks which live on the fabric.

I don't think so. Spacetime doesn't refer to the metric tensor, but to the manifold.

if you think that space time consists of some sort of particles that made up the "fabric" of spacetime, no this is not the case. Spacetime is the background stage where all the other particles perform their play. (Ok this might be way too poetic. )

However there are some theories not mainstream physics though, that claim that space time consists of particles.